The illustrated uniform composite circular rod is composed of a solid inner core with shear modulus μ₁ and a different outer core material of modulus μ₂. The two materials are assumed to be perfectly bonded at interface r = r₁, and thus the interfacial tangential displacements must be continuous uθ₁(r₁) = u_θ2(r₁). The composite shaft is to be loaded with an overall torque T. First justify that the angle of twists in each material must be the same and that torques in each material must satisfy T = T₁ + T₂. Next develop the torque-angle of twist relation:

and determine the stress τ,_θz in each material. Are these stresses continuous across the interface?
Finally establish a relationship between the torques T₁ and T₂ carried in each material.

Transcribed Image Text:

T = rm +(-11) M] 12]